LMFDB - Embedded newform 425.2.m.e.151.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(26,425)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("425.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.m (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			151.5
Character	$\chi$	$=$	425.151
Dual form			425.2.m.e.76.5

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.23200 + 1.23200i) q^{2} +(-0.229112 - 0.553124i) q^{3} +1.03565i q^{4} +(0.399184 - 0.963715i) q^{6} +(0.958968 + 0.397218i) q^{7} +(1.18808 - 1.18808i) q^{8} +(1.86787 - 1.86787i) q^{9} +(0.0292605 - 0.0706410i) q^{11} +(0.572843 - 0.237279i) q^{12} +2.86011i q^{13} +(0.692077 + 1.67082i) q^{14} +4.99873 q^{16} +(4.05747 + 0.732781i) q^{17} +4.60242 q^{18} +(-2.96308 - 2.96308i) q^{19} -0.621436i q^{21} +(0.123079 - 0.0509809i) q^{22} +(-2.27724 + 5.49775i) q^{23} +(-0.929359 - 0.384953i) q^{24} +(-3.52366 + 3.52366i) q^{26} +(-3.12049 - 1.29255i) q^{27} +(-0.411378 + 0.993155i) q^{28} +(-0.0817180 + 0.0338487i) q^{29} +(-0.928823 - 2.24238i) q^{31} +(3.78228 + 3.78228i) q^{32} -0.0457772 q^{33} +(4.09601 + 5.90159i) q^{34} +(1.93445 + 1.93445i) q^{36} +(3.63988 + 8.78745i) q^{37} -7.30103i q^{38} +(1.58200 - 0.655285i) q^{39} +(-7.74202 - 3.20685i) q^{41} +(0.765609 - 0.765609i) q^{42} +(0.612604 - 0.612604i) q^{43} +(0.0731594 + 0.0303036i) q^{44} +(-9.57880 + 3.96767i) q^{46} -8.33326i q^{47} +(-1.14527 - 2.76492i) q^{48} +(-4.18791 - 4.18791i) q^{49} +(-0.524293 - 2.41217i) q^{51} -2.96207 q^{52} +(-2.89277 - 2.89277i) q^{53} +(-2.25202 - 5.43686i) q^{54} +(1.61126 - 0.667405i) q^{56} +(-0.960076 + 2.31783i) q^{57} +(-0.142378 - 0.0589750i) q^{58} +(-6.48348 + 6.48348i) q^{59} +(-0.266392 - 0.110343i) q^{61} +(1.61830 - 3.90692i) q^{62} +(2.53317 - 1.04927i) q^{63} -0.677928i q^{64} +(-0.0563975 - 0.0563975i) q^{66} -12.8961 q^{67} +(-0.758905 + 4.20211i) q^{68} +3.56268 q^{69} +(5.05320 + 12.1995i) q^{71} -4.43835i q^{72} +(-6.04988 + 2.50594i) q^{73} +(-6.34181 + 15.3105i) q^{74} +(3.06871 - 3.06871i) q^{76} +(0.0561197 - 0.0561197i) q^{77} +(2.75633 + 1.14171i) q^{78} +(3.99465 - 9.64395i) q^{79} -5.90253i q^{81} +(-5.58733 - 13.4890i) q^{82} +(6.86298 + 6.86298i) q^{83} +0.643590 q^{84} +1.50946 q^{86} +(0.0374451 + 0.0374451i) q^{87} +(-0.0491634 - 0.118691i) q^{88} +0.106159i q^{89} +(-1.13609 + 2.74276i) q^{91} +(-5.69374 - 2.35843i) q^{92} +(-1.02751 + 1.02751i) q^{93} +(10.2666 - 10.2666i) q^{94} +(1.22551 - 2.95863i) q^{96} +(-7.91737 + 3.27948i) q^{97} -10.3190i q^{98} +(-0.0772933 - 0.186603i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{9} + 24 q^{14} + 8 q^{16} + 24 q^{19} - 32 q^{24} - 16 q^{26} - 24 q^{29} - 24 q^{31} - 8 q^{34} + 8 q^{36} + 24 q^{39} - 48 q^{41} - 72 q^{44} - 16 q^{46} - 48 q^{49} - 32 q^{54} + 24 q^{56}+ \cdots + 80 q^{99}+O(q^{100}) $ 24 * q + 8 * q^9 + 24 * q^14 + 8 * q^16 + 24 * q^19 - 32 * q^24 - 16 * q^26 - 24 * q^29 - 24 * q^31 - 8 * q^34 + 8 * q^36 + 24 * q^39 - 48 * q^41 - 72 * q^44 - 16 * q^46 - 48 * q^49 - 32 * q^54 + 24 * q^56 + 48 * q^59 + 16 * q^61 - 96 * q^66 - 32 * q^69 + 16 * q^71 + 64 * q^74 - 24 * q^76 + 72 * q^79 + 96 * q^84 - 8 * q^91 + 40 * q^94 + 96 * q^96 + 80 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.23200	+	1.23200i	0.871156	+	0.871156i	0.992598	−	0.121443i	$-0.0387521\pi$
$2$	1.23200	+	1.23200i	0.871156	+	0.871156i	−0.121443	+	0.992598i	$0.538752\pi$
$3$	−0.229112	−	0.553124i	−0.132278	−	0.319347i	0.843838	−	0.536598i	$-0.180291\pi$
$3$	−0.229112	−	0.553124i	−0.132278	−	0.319347i	−0.976116	+	0.217251i	$0.930291\pi$
$4$			1.03565i			0.517825i
$5$		0			0
$5$		0			0
$6$	0.399184	−	0.963715i	0.162966	−	0.393435i
$7$	0.958968	+	0.397218i	0.362456	+	0.150134i	0.556477	−	0.830863i	$-0.312153\pi$
$7$	0.958968	+	0.397218i	0.362456	+	0.150134i	−0.194021	+	0.980997i	$0.562153\pi$
$8$	1.18808	−	1.18808i	0.420050	−	0.420050i
$9$	1.86787	−	1.86787i	0.622622	−	0.622622i
$10$		0			0
$11$	0.0292605	−	0.0706410i	0.00882236	−	0.0212991i	−0.919407	−	0.393308i	$-0.871331\pi$
$11$	0.0292605	−	0.0706410i	0.00882236	−	0.0212991i	0.928229	+	0.372008i	$0.121331\pi$
$12$	0.572843	−	0.237279i	0.165366	−	0.0684966i
$13$			2.86011i			0.793252i	0.917980	+	0.396626i	$0.129819\pi$
$13$			2.86011i			0.793252i	−0.917980	+	0.396626i	$0.870181\pi$
$14$	0.692077	+	1.67082i	0.184965	+	0.446546i
$15$		0			0
$16$	4.99873			1.24968
$17$	4.05747	+	0.732781i	0.984080	+	0.177726i
$17$	4.05747	+	0.732781i	0.984080	+	0.177726i
$18$	4.60242			1.08480
$19$	−2.96308	−	2.96308i	−0.679777	−	0.679777i	0.280173	−	0.959950i	$-0.409608\pi$
$19$	−2.96308	−	2.96308i	−0.679777	−	0.679777i	−0.959950	+	0.280173i	$0.909608\pi$
$20$		0			0
$21$		−	0.621436i		−	0.135608i
$22$	0.123079	−	0.0509809i	0.0262405	−	0.0108692i
$23$	−2.27724	+	5.49775i	−0.474838	+	1.14636i	0.487162	+	0.873312i	$0.338032\pi$
$23$	−2.27724	+	5.49775i	−0.474838	+	1.14636i	−0.962000	+	0.273049i	$0.911968\pi$
$24$	−0.929359	−	0.384953i	−0.189705	−	0.0785782i
$25$		0			0
$26$	−3.52366	+	3.52366i	−0.691046	+	0.691046i
$27$	−3.12049	−	1.29255i	−0.600538	−	0.248751i
$28$	−0.411378	+	0.993155i	−0.0777432	+	0.187689i
$29$	−0.0817180	+	0.0338487i	−0.0151747	+	0.00628555i	−0.390258	−	0.920706i	$-0.627614\pi$
$29$	−0.0817180	+	0.0338487i	−0.0151747	+	0.00628555i	0.375083	+	0.926991i	$0.377614\pi$
$30$		0			0
$31$	−0.928823	−	2.24238i	−0.166822	−	0.402743i	0.818256	−	0.574854i	$-0.194941\pi$
$31$	−0.928823	−	2.24238i	−0.166822	−	0.402743i	−0.985078	+	0.172111i	$0.944941\pi$
$32$	3.78228	+	3.78228i	0.668618	+	0.668618i
$33$	−0.0457772			−0.00796879
$34$	4.09601	+	5.90159i	0.702460	+	1.01211i
$35$		0			0
$36$	1.93445	+	1.93445i	0.322409	+	0.322409i
$37$	3.63988	+	8.78745i	0.598393	+	1.44465i	0.875218	+	0.483728i	$0.160718\pi$
$37$	3.63988	+	8.78745i	0.598393	+	1.44465i	−0.276826	+	0.960920i	$0.589282\pi$
$38$		−	7.30103i		−	1.18438i
$39$	1.58200	−	0.655285i	0.253322	−	0.104930i
$40$		0			0
$41$	−7.74202	−	3.20685i	−1.20910	−	0.500826i	−0.315172	−	0.949035i	$-0.602062\pi$
$41$	−7.74202	−	3.20685i	−1.20910	−	0.500826i	−0.893929	+	0.448209i	$0.852062\pi$
$42$	0.765609	−	0.765609i	0.118136	−	0.118136i
$43$	0.612604	−	0.612604i	0.0934212	−	0.0934212i	−0.658852	−	0.752273i	$-0.728958\pi$
$43$	0.612604	−	0.612604i	0.0934212	−	0.0934212i	0.752273	+	0.658852i	$0.228958\pi$
$44$	0.0731594	+	0.0303036i	0.0110292	+	0.00456844i
$45$		0			0
$46$	−9.57880	+	3.96767i	−1.41232	+	0.585001i
$47$		−	8.33326i		−	1.21553i	−0.794117	−	0.607765i	$-0.792066\pi$
$47$		−	8.33326i		−	1.21553i	0.794117	−	0.607765i	$-0.207934\pi$
$48$	−1.14527	−	2.76492i	−0.165305	−	0.399082i
$49$	−4.18791	−	4.18791i	−0.598273	−	0.598273i
$50$		0			0
$51$	−0.524293	−	2.41217i	−0.0734158	−	0.337772i
$52$	−2.96207			−0.410766
$53$	−2.89277	−	2.89277i	−0.397353	−	0.397353i	0.479946	−	0.877298i	$-0.340656\pi$
$53$	−2.89277	−	2.89277i	−0.397353	−	0.397353i	−0.877298	+	0.479946i	$0.840656\pi$
$54$	−2.25202	−	5.43686i	−0.306461	−	0.739863i
$55$		0			0
$56$	1.61126	−	0.667405i	0.215313	−	0.0891857i
$57$	−0.960076	+	2.31783i	−0.127165	+	0.307004i
$58$	−0.142378	−	0.0589750i	−0.0186952	−	0.00774379i
$59$	−6.48348	+	6.48348i	−0.844078	+	0.844078i	−0.989386	−	0.145309i	$-0.953582\pi$
$59$	−6.48348	+	6.48348i	−0.844078	+	0.844078i	0.145309	+	0.989386i	$0.453582\pi$
$60$		0			0
$61$	−0.266392	−	0.110343i	−0.0341080	−	0.0141280i	0.365564	−	0.930786i	$-0.380876\pi$
$61$	−0.266392	−	0.110343i	−0.0341080	−	0.0141280i	−0.399672	+	0.916658i	$0.630876\pi$
$62$	1.61830	−	3.90692i	0.205524	−	0.496179i
$63$	2.53317	−	1.04927i	0.319150	−	0.132196i
$64$		−	0.677928i		−	0.0847410i
$65$		0			0
$66$	−0.0563975	−	0.0563975i	−0.00694205	−	0.00694205i
$67$	−12.8961			−1.57551			−0.787755	−	0.615988i	$-0.788757\pi$
$67$	−12.8961			−1.57551			−0.787755	+	0.615988i	$0.788757\pi$
$68$	−0.758905	+	4.20211i	−0.0920307	+	0.509581i
$69$	3.56268			0.428897
$70$		0			0
$71$	5.05320	+	12.1995i	0.599704	+	1.44781i	0.873883	+	0.486135i	$0.161594\pi$
$71$	5.05320	+	12.1995i	0.599704	+	1.44781i	−0.274179	+	0.961679i	$0.588406\pi$
$72$		−	4.43835i		−	0.523064i
$73$	−6.04988	+	2.50594i	−0.708085	+	0.293298i	−0.707512	−	0.706701i	$-0.750182\pi$
$73$	−6.04988	+	2.50594i	−0.708085	+	0.293298i	−0.000573207		1.00000i	$0.500182\pi$
$74$	−6.34181	+	15.3105i	−0.737220	+	1.77981i
$75$		0			0
$76$	3.06871	−	3.06871i	0.352005	−	0.352005i
$77$	0.0561197	−	0.0561197i	0.00639544	−	0.00639544i
$78$	2.75633	+	1.14171i	0.312093	+	0.129273i
$79$	3.99465	−	9.64395i	0.449434	−	1.08503i	−0.523101	−	0.852271i	$-0.675225\pi$
$79$	3.99465	−	9.64395i	0.449434	−	1.08503i	0.972535	−	0.232758i	$-0.0747751\pi$
$80$		0			0
$81$		−	5.90253i		−	0.655837i
$82$	−5.58733	−	13.4890i	−0.617018	−	1.48961i
$83$	6.86298	+	6.86298i	0.753310	+	0.753310i	0.975095	−	0.221786i	$-0.0711886\pi$
$83$	6.86298	+	6.86298i	0.753310	+	0.753310i	−0.221786	+	0.975095i	$0.571189\pi$
$84$	0.643590			0.0702214
$85$		0			0
$86$	1.50946			0.162769
$87$	0.0374451	+	0.0374451i	0.00401453	+	0.00401453i
$88$	−0.0491634	−	0.118691i	−0.00524084	−	0.0126525i
$89$			0.106159i			0.0112528i	0.999984	+	0.00562641i	$0.00179095\pi$
$89$			0.106159i			0.0112528i	−0.999984	+	0.00562641i	$0.998209\pi$
$90$		0			0
$91$	−1.13609	+	2.74276i	−0.119094	+	0.287519i
$92$	−5.69374	−	2.35843i	−0.593614	−	0.245883i
$93$	−1.02751	+	1.02751i	−0.106548	+	0.106548i
$94$	10.2666	−	10.2666i	1.05892	−	1.05892i
$95$		0			0
$96$	1.22551	−	2.95863i	0.125078	−	0.301964i
$97$	−7.91737	+	3.27948i	−0.803888	+	0.332981i	−0.746512	−	0.665372i	$-0.768273\pi$
$97$	−7.91737	+	3.27948i	−0.803888	+	0.332981i	−0.0573752	+	0.998353i	$0.518273\pi$
$98$		−	10.3190i		−	1.04238i
$99$	−0.0772933	−	0.186603i	−0.00776827	−	0.0187543i
$100$		0			0
$101$	8.51123			0.846899			0.423449	−	0.905920i	$-0.360819\pi$
$101$	8.51123			0.846899			0.423449	+	0.905920i	$0.360819\pi$
$102$	2.32587	−	3.61773i	0.230295	−	0.358208i
$103$	−11.9713			−1.17956			−0.589782	−	0.807563i	$-0.700786\pi$
$103$	−11.9713			−1.17956			−0.589782	+	0.807563i	$0.700786\pi$
$104$	3.39804	+	3.39804i	0.333205	+	0.333205i
$105$		0			0
$106$		−	7.12779i		−	0.692312i
$107$	−18.1985	+	7.53806i	−1.75931	+	0.728732i	−0.762677	+	0.646779i	$0.776116\pi$
$107$	−18.1985	+	7.53806i	−1.75931	+	0.728732i	−0.996636	+	0.0819523i	$0.973884\pi$
$108$	1.33863	−	3.23173i	0.128809	−	0.310973i
$109$	2.36163	+	0.978218i	0.226203	+	0.0936963i	0.492906	−	0.870082i	$-0.335934\pi$
$109$	2.36163	+	0.978218i	0.226203	+	0.0936963i	−0.266704	+	0.963779i	$0.585934\pi$
$110$		0			0
$111$	4.02661	−	4.02661i	0.382189	−	0.382189i
$112$	4.79362	+	1.98558i	0.452955	+	0.187620i
$113$	−0.337421	+	0.814605i	−0.0317419	+	0.0766316i	−0.938956	−	0.344038i	$-0.888205\pi$
$113$	−0.337421	+	0.814605i	−0.0317419	+	0.0766316i	0.907214	+	0.420670i	$0.138205\pi$
$114$	−4.03838	+	1.67275i	−0.378229	+	0.156667i
$115$		0			0
$116$	−0.0350554	−	0.0846312i	−0.00325481	−	0.00785781i
$117$	5.34230	+	5.34230i	0.493896	+	0.493896i
$118$	−15.9753			−1.47065
$119$	3.59991	+	2.31441i	0.330003	+	0.212162i
$120$		0			0
$121$	7.77404	+	7.77404i	0.706731	+	0.706731i
$122$	−0.192252	−	0.464137i	−0.0174057	−	0.0420210i
$123$			5.01703i			0.452370i
$124$	2.32232	−	0.961935i	0.208550	−	0.0863843i
$125$		0			0
$126$	4.41358	+	1.82816i	0.393193	+	0.162866i
$127$	11.8681	−	11.8681i	1.05312	−	1.05312i	0.0546149	−	0.998507i	$-0.482607\pi$
$127$	11.8681	−	11.8681i	1.05312	−	1.05312i	0.998507	−	0.0546149i	$-0.0173931\pi$
$128$	8.39976	−	8.39976i	0.742441	−	0.742441i
$129$	−0.479201	−	0.198491i	−0.0421913	−	0.0174762i
$130$		0			0
$131$	7.85656	−	3.25429i	0.686431	−	0.284329i	−0.0120814	−	0.999927i	$-0.503846\pi$
$131$	7.85656	−	3.25429i	0.686431	−	0.284329i	0.698512	+	0.715598i	$0.253846\pi$
$132$		−	0.0474091i		−	0.00412644i
$133$	−1.66451	−	4.01849i	−0.144331	−	0.348447i
$134$	−15.8880	−	15.8880i	−1.37252	−	1.37252i
$135$		0			0
$136$	5.69120	−	3.94999i	0.488016	−	0.338709i
$137$	15.5810			1.33117			0.665585	−	0.746322i	$-0.268182\pi$
$137$	15.5810			1.33117			0.665585	+	0.746322i	$0.268182\pi$
$138$	4.38923	+	4.38923i	0.373636	+	0.373636i
$139$	3.00131	+	7.24579i	0.254567	+	0.614580i	0.998562	−	0.0536052i	$-0.0170713\pi$
$139$	3.00131	+	7.24579i	0.254567	+	0.614580i	−0.743995	+	0.668185i	$0.767071\pi$
$140$		0			0
$141$	−4.60933	+	1.90925i	−0.388176	+	0.160788i
$142$	−8.80424	+	21.2553i	−0.738836	+	1.78371i
$143$	0.202041	+	0.0836882i	0.0168955	+	0.00699836i
$144$	9.33696	−	9.33696i	0.778080	−	0.778080i
$145$		0			0
$146$	−10.5408	−	4.36613i	−0.872361	−	0.361344i
$147$	−1.35694	+	3.27593i	−0.111918	+	0.270194i
$148$	−9.10072	+	3.76964i	−0.748075	+	0.309863i
$149$			20.5823i			1.68616i	0.537785	+	0.843082i	$0.319261\pi$
$149$			20.5823i			1.68616i	−0.537785	+	0.843082i	$0.680739\pi$
$150$		0			0
$151$	−10.2462	−	10.2462i	−0.833824	−	0.833824i	0.154213	−	0.988038i	$-0.450716\pi$
$151$	−10.2462	−	10.2462i	−0.833824	−	0.833824i	−0.988038	+	0.154213i	$0.950716\pi$
$152$	−7.04075			−0.571080
$153$	8.94754	−	6.21007i	0.723366	−	0.502054i
$154$	0.138279			0.0111428
$155$		0			0
$156$	0.678645	+	1.63839i	0.0543351	+	0.131177i
$157$		−	11.6355i		−	0.928611i	−0.885675	−	0.464306i	$-0.846304\pi$
$157$		−	11.6355i		−	0.928611i	0.885675	−	0.464306i	$-0.153696\pi$
$158$	16.8028	−	6.95993i	1.33676	−	0.553702i
$159$	−0.937295	+	2.26283i	−0.0743323	+	0.179454i
$160$		0			0
$161$	−4.36761	+	4.36761i	−0.344216	+	0.344216i
$162$	7.27192	−	7.27192i	0.571336	−	0.571336i
$163$	−9.55043	−	3.95592i	−0.748047	−	0.309851i	−0.0241026	−	0.999709i	$-0.507673\pi$
$163$	−9.55043	−	3.95592i	−0.748047	−	0.309851i	−0.723944	+	0.689858i	$0.757673\pi$
$164$	3.32117	−	8.01802i	0.259340	−	0.626102i
$165$		0			0
$166$			16.9104i			1.31250i
$167$	−5.06719	−	12.2333i	−0.392111	−	0.946639i	−0.989480	−	0.144672i	$-0.953787\pi$
$167$	−5.06719	−	12.2333i	−0.392111	−	0.946639i	0.597369	−	0.801967i	$-0.296213\pi$
$168$	−0.738316	−	0.738316i	−0.0569623	−	0.0569623i
$169$	4.81976			0.370751
$170$		0			0
$171$	−11.0693			−0.846488
$172$	0.634443	+	0.634443i	0.0483758	+	0.0483758i
$173$	8.63998	+	20.8588i	0.656886	+	1.58586i	0.802588	+	0.596534i	$0.203456\pi$
$173$	8.63998	+	20.8588i	0.656886	+	1.58586i	−0.145703	+	0.989328i	$0.546544\pi$
$174$			0.0922647i			0.00699457i
$175$		0			0
$176$	0.146265	−	0.353115i	0.0110252	−	0.0266171i
$177$	5.07161	+	2.10073i	0.381206	+	0.157901i
$178$	−0.130788	+	0.130788i	−0.00980296	+	0.00980296i
$179$	3.77815	−	3.77815i	0.282392	−	0.282392i	−0.551670	−	0.834062i	$-0.686009\pi$
$179$	3.77815	−	3.77815i	0.282392	−	0.282392i	0.834062	+	0.551670i	$0.186009\pi$
$180$		0			0
$181$	0.772220	−	1.86430i	0.0573987	−	0.138573i	−0.892578	−	0.450892i	$-0.851106\pi$
$181$	0.772220	−	1.86430i	0.0573987	−	0.138573i	0.949977	+	0.312319i	$0.101106\pi$
$182$	−4.77874	+	1.97942i	−0.354223	+	0.146724i
$183$			0.172629i			0.0127611i
$184$	3.82622	+	9.23732i	0.282073	+	0.680984i
$185$		0			0
$186$	−2.53178			−0.185639
$187$	0.170488	−	0.265182i	0.0124673	−	0.0193920i
$188$	8.63034			0.629432
$189$	−2.47902	−	2.47902i	−0.180322	−	0.180322i
$190$		0			0
$191$			12.8742i			0.931547i	0.884904	+	0.465774i	$0.154224\pi$
$191$			12.8742i			0.931547i	−0.884904	+	0.465774i	$0.845776\pi$
$192$	−0.374979	+	0.155321i	−0.0270618	+	0.0112093i
$193$	−1.01693	+	2.45509i	−0.0732004	+	0.176721i	−0.956245	−	0.292569i	$-0.905490\pi$
$193$	−1.01693	+	2.45509i	−0.0732004	+	0.176721i	0.883044	+	0.469290i	$0.155490\pi$
$194$	−13.7945	−	5.71388i	−0.990390	−	0.410233i
$195$		0			0
$196$	4.33721	−	4.33721i	0.309800	−	0.309800i
$197$	16.0056	+	6.62975i	1.14035	+	0.472350i	0.871288	−	0.490771i	$-0.163285\pi$
$197$	16.0056	+	6.62975i	1.14035	+	0.472350i	0.269066	+	0.963122i	$0.413285\pi$
$198$	0.134669	−	0.325120i	0.00957051	−	0.0231053i
$199$	−21.1017	+	8.74062i	−1.49586	+	0.619606i	−0.972583	−	0.232556i	$-0.925291\pi$
$199$	−21.1017	+	8.74062i	−1.49586	+	0.619606i	−0.523278	+	0.852162i	$0.675291\pi$
$200$		0			0
$201$	2.95465	+	7.13315i	0.208405	+	0.503134i
$202$	10.4858	+	10.4858i	0.737781	+	0.737781i
$203$	−0.0918103			−0.00644382
$204$	2.49817	−	0.542984i	0.174907	−	0.0380165i
$205$		0			0
$206$	−14.7486	−	14.7486i	−1.02758	−	1.02758i
$207$	6.01548	+	14.5226i	0.418105	+	1.00939i
$208$			14.2969i			0.991313i
$209$	−0.296016	+	0.122614i	−0.0204759	+	0.00848138i
$210$		0			0
$211$	−2.75762	−	1.14224i	−0.189843	−	0.0786354i	0.285737	−	0.958308i	$-0.407762\pi$
$211$	−2.75762	−	1.14224i	−0.189843	−	0.0786354i	−0.475580	+	0.879673i	$0.657762\pi$
$212$	2.99590	−	2.99590i	0.205759	−	0.205759i
$213$	5.59009	−	5.59009i	0.383027	−	0.383027i
$214$	−31.7074	−	13.1336i	−2.16747	−	0.897797i
$215$		0			0
$216$	−5.24304	+	2.17174i	−0.356743	+	0.147768i
$217$		−	2.51931i		−	0.171022i
$218$	1.70436	+	4.11469i	0.115434	+	0.278682i
$219$	2.77220	+	2.77220i	0.187328	+	0.187328i
$220$		0			0
$221$	−2.09584	+	11.6048i	−0.140981	+	0.780624i
$222$	9.92158			0.665893
$223$	−2.87618	−	2.87618i	−0.192603	−	0.192603i	0.604217	−	0.796820i	$-0.293486\pi$
$223$	−2.87618	−	2.87618i	−0.192603	−	0.192603i	−0.796820	+	0.604217i	$0.793486\pi$
$224$	2.12470	+	5.12947i	0.141962	+	0.342727i
$225$		0			0
$226$	−1.41930	+	0.587892i	−0.0944102	+	0.0391060i
$227$	−3.17460	+	7.66416i	−0.210705	+	0.508688i	−0.993532	−	0.113552i	$-0.963777\pi$
$227$	−3.17460	+	7.66416i	−0.210705	+	0.508688i	0.782827	+	0.622240i	$0.213777\pi$
$228$	−2.40046	−	0.994302i	−0.158974	−	0.0658492i
$229$	3.07003	−	3.07003i	0.202874	−	0.202874i	−0.598356	−	0.801230i	$-0.704179\pi$
$229$	3.07003	−	3.07003i	0.202874	−	0.202874i	0.801230	+	0.598356i	$0.204179\pi$
$230$		0			0
$231$	−0.0438989	−	0.0181835i	−0.00288833	−	0.00119639i
$232$	−0.0568726	+	0.137302i	−0.00373387	+	0.00901435i
$233$	−0.0251958	+	0.0104364i	−0.00165063	+	0.000683713i	−0.383509	−	0.923537i	$-0.625284\pi$
$233$	−0.0251958	+	0.0104364i	−0.00165063	+	0.000683713i	0.381858	+	0.924221i	$0.375284\pi$
$234$			13.1634i			0.860521i
$235$		0			0
$236$	−6.71462	−	6.71462i	−0.437084	−	0.437084i
$237$	−6.24952			−0.405950
$238$	1.58373	+	7.28644i	0.102658	+	0.472310i
$239$	15.9333			1.03064			0.515320	−	0.856998i	$-0.327673\pi$
$239$	15.9333			1.03064			0.515320	+	0.856998i	$0.327673\pi$
$240$		0			0
$241$	−5.46731	−	13.1993i	−0.352180	−	0.850239i	−0.996350	−	0.0853566i	$-0.972797\pi$
$241$	−5.46731	−	13.1993i	−0.352180	−	0.850239i	0.644170	−	0.764882i	$-0.277203\pi$
$242$			19.1552i			1.23135i
$243$	−12.6263	+	5.22998i	−0.809977	+	0.335503i
$244$	0.114277	−	0.275888i	0.00731582	−	0.0176619i
$245$		0			0
$246$	−6.18098	+	6.18098i	−0.394085	+	0.394085i
$247$	8.47474	−	8.47474i	0.539235	−	0.539235i
$248$	−3.76764	−	1.56061i	−0.239245	−	0.0990987i
$249$	2.22369	−	5.36847i	0.140921	−	0.340213i
$250$		0			0
$251$			8.16222i			0.515195i	0.966252	+	0.257597i	$0.0829308\pi$
$251$			8.16222i			0.515195i	−0.966252	+	0.257597i	$0.917069\pi$
$252$	1.08668	+	2.62348i	0.0684545	+	0.165264i
$253$	0.321734	+	0.321734i	0.0202272	+	0.0202272i
$254$	29.2430			1.83487
$255$		0			0
$256$	19.3412			1.20882
$257$	6.91898	+	6.91898i	0.431594	+	0.431594i	0.889170	−	0.457576i	$-0.151282\pi$
$257$	6.91898	+	6.91898i	0.431594	+	0.431594i	−0.457576	+	0.889170i	$0.651282\pi$
$258$	−0.345834	−	0.834917i	−0.0215307	−	0.0519796i
$259$			9.87271i			0.613461i
$260$		0			0
$261$	−0.0894134	+	0.215863i	−0.00553455	+	0.0133616i
$262$	13.6886	+	5.66999i	0.845683	+	0.350293i
$263$	10.0516	−	10.0516i	0.619809	−	0.619809i	−0.325673	−	0.945482i	$-0.605591\pi$
$263$	10.0516	−	10.0516i	0.619809	−	0.619809i	0.945482	+	0.325673i	$0.105591\pi$
$264$	−0.0543870	+	0.0543870i	−0.00334729	+	0.00334729i
$265$		0			0
$266$	2.90010	−	7.00146i	0.177816	−	0.429287i
$267$	0.0587191	−	0.0243222i	0.00359355	−	0.00148850i
$268$		−	13.3559i		−	0.815839i
$269$	−8.71283	−	21.0346i	−0.531231	−	1.28250i	−0.930709	−	0.365762i	$-0.880809\pi$
$269$	−8.71283	−	21.0346i	−0.531231	−	1.28250i	0.399478	−	0.916743i	$-0.369191\pi$
$270$		0			0
$271$	−17.6024			−1.06927			−0.534636	−	0.845083i	$-0.679551\pi$
$271$	−17.6024			−1.06927			−0.534636	+	0.845083i	$0.679551\pi$
$272$	20.2822	+	3.66298i	1.22979	+	0.222101i
$273$	1.77738			0.107572
$274$	19.1957	+	19.1957i	1.15966	+	1.15966i
$275$		0			0
$276$			3.68969i			0.222093i
$277$	−6.22351	+	2.57786i	−0.373934	+	0.154889i	−0.561732	−	0.827319i	$-0.689865\pi$
$277$	−6.22351	+	2.57786i	−0.373934	+	0.154889i	0.187798	+	0.982208i	$0.439865\pi$
$278$	−5.22921	+	12.6244i	−0.313627	+	0.757163i
$279$	−5.92338	−	2.45354i	−0.354623	−	0.146890i
$280$		0			0
$281$	16.2410	−	16.2410i	0.968854	−	0.968854i	−0.0306751	−	0.999529i	$-0.509766\pi$
$281$	16.2410	−	16.2410i	0.968854	−	0.968854i	0.999529	+	0.0306751i	$0.00976573\pi$
$282$	−8.03089	−	3.32650i	−0.478232	−	0.198090i
$283$	7.41233	−	17.8949i	0.440617	−	1.06374i	−0.535115	−	0.844779i	$-0.679732\pi$
$283$	7.41233	−	17.8949i	0.440617	−	1.06374i	0.975733	−	0.218965i	$-0.0702681\pi$
$284$	−12.6344	+	5.23334i	−0.749714	+	0.310542i
$285$		0			0
$286$	0.145811	+	0.352019i	0.00862198	+	0.0208153i
$287$	−6.15054	−	6.15054i	−0.363055	−	0.363055i
$288$	14.1296			0.832593
$289$	15.9261	+	5.94647i	0.936827	+	0.349792i
$290$		0			0
$291$	3.62792	+	3.62792i	0.212673	+	0.212673i
$292$	−2.59528	−	6.26556i	−0.151877	−	0.366664i
$293$		−	20.2095i		−	1.18065i	−0.807164	−	0.590327i	$-0.798999\pi$
$293$		−	20.2095i		−	1.18065i	0.807164	−	0.590327i	$-0.201001\pi$
$294$	−5.70770	+	2.36421i	−0.332880	+	0.137883i
$295$		0			0
$296$	14.7647	+	6.11572i	0.858179	+	0.355469i
$297$	−0.182614	+	0.182614i	−0.0105963	+	0.0105963i
$298$	−25.3573	+	25.3573i	−1.46891	+	1.46891i
$299$	−15.7242	−	6.51317i	−0.909353	−	0.376666i
$300$		0			0
$301$	0.830805	−	0.344131i	0.0478868	−	0.0198354i
$302$		−	25.2466i		−	1.45278i
$303$	−1.95002	−	4.70777i	−0.112026	−	0.270454i
$304$	−14.8116	−	14.8116i	−0.849505	−	0.849505i
$305$		0			0
$306$	18.6742	+	3.37257i	1.06753	+	0.192797i
$307$	−18.0835			−1.03208			−0.516039	−	0.856565i	$-0.672594\pi$
$307$	−18.0835			−1.03208			−0.516039	+	0.856565i	$0.672594\pi$
$308$	0.0581204	+	0.0581204i	0.00331172	+	0.00331172i
$309$	2.74276	+	6.62160i	0.156030	+	0.376690i
$310$		0			0
$311$	18.8979	−	7.82776i	1.07160	−	0.443872i	0.224046	−	0.974579i	$-0.428073\pi$
$311$	18.8979	−	7.82776i	1.07160	−	0.443872i	0.847555	+	0.530707i	$0.178073\pi$
$312$	1.10101	−	2.65807i	0.0623323	−	0.150484i
$313$	21.9797	+	9.10430i	1.24237	+	0.514606i	0.904454	−	0.426571i	$-0.140279\pi$
$313$	21.9797	+	9.10430i	1.24237	+	0.514606i	0.337914	+	0.941177i	$0.390279\pi$
$314$	14.3349	−	14.3349i	0.808965	−	0.808965i
$315$		0			0
$316$	9.98775	+	4.13706i	0.561855	+	0.232728i
$317$	2.00203	−	4.83333i	0.112445	−	0.271467i	−0.857632	−	0.514264i	$-0.828065\pi$
$317$	2.00203	−	4.83333i	0.112445	−	0.271467i	0.970077	+	0.242798i	$0.0780651\pi$
$318$	−3.94256	+	1.63306i	−0.221088	+	0.0915774i
$319$			0.00676307i			0.000378659i
$320$		0			0
$321$	8.33897	+	8.33897i	0.465436	+	0.465436i
$322$	−10.7618			−0.599731
$323$	−9.85131	−	14.1939i	−0.548141	−	0.789769i
$324$	6.11295			0.339608
$325$		0			0
$326$	−6.89244	−	16.6398i	−0.381737	−	0.921594i
$327$		−	1.53040i		−	0.0846310i
$328$	−13.0081	+	5.38815i	−0.718254	+	0.297511i
$329$	3.31012	−	7.99133i	0.182493	−	0.440576i
$330$		0			0
$331$	17.8508	−	17.8508i	0.981168	−	0.981168i	−0.0186578	−	0.999826i	$-0.505939\pi$
$331$	17.8508	−	17.8508i	0.981168	−	0.981168i	0.999826	+	0.0186578i	$0.00593929\pi$
$332$	−7.10764	+	7.10764i	−0.390082	+	0.390082i
$333$	23.2126	+	9.61497i	1.27204	+	0.526897i
$334$	8.82862	−	21.3142i	0.483080	−	1.16626i
$335$		0			0
$336$		−	3.10639i		−	0.169467i
$337$	0.227143	+	0.548372i	0.0123733	+	0.0298717i	0.929945	−	0.367698i	$-0.119854\pi$
$337$	0.227143	+	0.548372i	0.0123733	+	0.0298717i	−0.917572	+	0.397569i	$0.869854\pi$
$338$	5.93795	+	5.93795i	0.322982	+	0.322982i
$339$	0.527885			0.0286708
$340$		0			0
$341$	−0.185582			−0.0100498
$342$	−13.6373	−	13.6373i	−0.737423	−	0.737423i
$343$	−5.13308	−	12.3924i	−0.277161	−	0.669125i
$344$		−	1.45564i		−	0.0784831i
$345$		0			0
$346$	−15.0535	+	36.3425i	−0.809283	+	1.95378i
$347$	−1.87926	−	0.778415i	−0.100884	−	0.0417875i	0.331671	−	0.943395i	$-0.392388\pi$
$347$	−1.87926	−	0.778415i	−0.100884	−	0.0417875i	−0.432555	+	0.901608i	$0.642388\pi$
$348$	−0.0387800	+	0.0387800i	−0.00207883	+	0.00207883i
$349$	−2.09333	+	2.09333i	−0.112053	+	0.112053i	−0.760910	−	0.648857i	$-0.775247\pi$
$349$	−2.09333	+	2.09333i	−0.112053	+	0.112053i	0.648857	+	0.760910i	$0.275247\pi$
$350$		0			0
$351$	3.69683	−	8.92493i	0.197322	−	0.476378i
$352$	0.377855	−	0.156513i	0.0201397	−	0.00834215i
$353$			16.0575i			0.854656i	0.904097	+	0.427328i	$0.140545\pi$
$353$			16.0575i			0.854656i	−0.904097	+	0.427328i	$0.859455\pi$
$354$	3.66013	+	8.83633i	0.194534	+	0.469646i
$355$		0			0
$356$	−0.109943			−0.00582699
$357$	0.455377	−	2.52146i	0.0241011	−	0.133450i
$358$	9.30937			0.492015
$359$	14.3396	+	14.3396i	0.756815	+	0.756815i	0.975741	−	0.218926i	$-0.0702555\pi$
$359$	14.3396	+	14.3396i	0.756815	+	0.756815i	−0.218926	+	0.975741i	$0.570255\pi$
$360$		0			0
$361$		−	1.44032i		−	0.0758063i
$362$	3.24820	−	1.34545i	0.170722	−	0.0707152i
$363$	2.51889	−	6.08113i	0.132207	−	0.319177i
$364$	−2.84053	−	1.17659i	−0.148884	−	0.0616700i
$365$		0			0
$366$	−0.212678	+	0.212678i	−0.0111169	+	0.0111169i
$367$	−18.9978	−	7.86915i	−0.991678	−	0.410767i	−0.172939	−	0.984933i	$-0.555326\pi$
$367$	−18.9978	−	7.86915i	−0.991678	−	0.410767i	−0.818739	+	0.574166i	$0.805326\pi$
$368$	−11.3833	+	27.4818i	−0.593397	+	1.43259i
$369$	−20.4510	+	8.47109i	−1.06464	+	0.440987i
$370$		0			0
$371$	−1.62502	−	3.92314i	−0.0843667	−	0.203679i
$372$	−1.06414	−	1.06414i	−0.0551731	−	0.0551731i
$373$	−5.43210			−0.281264			−0.140632	−	0.990062i	$-0.544913\pi$
$373$	−5.43210			−0.281264			−0.140632	+	0.990062i	$0.544913\pi$
$374$	0.536745	−	0.116663i	0.0277544	−	0.00603252i
$375$		0			0
$376$	−9.90058	−	9.90058i	−0.510583	−	0.510583i
$377$	−0.0968111	−	0.233723i	−0.00498602	−	0.0120373i
$378$		−	6.10832i		−	0.314178i
$379$	18.0688	−	7.48435i	0.928133	−	0.384445i	0.133163	−	0.991094i	$-0.457487\pi$
$379$	18.0688	−	7.48435i	0.928133	−	0.384445i	0.794970	+	0.606649i	$0.207487\pi$
$380$		0			0
$381$	−9.28364	−	3.84541i	−0.475616	−	0.197006i
$382$	−15.8611	+	15.8611i	−0.811523	+	0.811523i
$383$	7.79547	−	7.79547i	0.398330	−	0.398330i	−0.479314	−	0.877644i	$-0.659114\pi$
$383$	7.79547	−	7.79547i	0.398330	−	0.398330i	0.877644	+	0.479314i	$0.159114\pi$
$384$	−6.57059	−	2.72163i	−0.335304	−	0.138888i
$385$		0			0
$386$	−4.27753	+	1.77181i	−0.217721	+	0.0901829i
$387$		−	2.28852i		−	0.116332i
$388$	−3.39640	−	8.19962i	−0.172426	−	0.416273i
$389$	−7.61741	−	7.61741i	−0.386218	−	0.386218i	0.487118	−	0.873336i	$-0.338048\pi$
$389$	−7.61741	−	7.61741i	−0.386218	−	0.386218i	−0.873336	+	0.487118i	$0.838048\pi$
$390$		0			0
$391$	−13.2685	+	20.6382i	−0.671016	+	1.04372i
$392$	−9.95114			−0.502609
$393$	−3.60006	−	3.60006i	−0.181599	−	0.181599i
$394$	11.5511	+	27.8868i	0.581936	+	1.40492i
$395$		0			0
$396$	0.193255	−	0.0800488i	0.00971143	−	0.00402260i
$397$	2.52765	−	6.10228i	0.126859	−	0.306265i	−0.847671	−	0.530522i	$-0.821996\pi$
$397$	2.52765	−	6.10228i	0.126859	−	0.306265i	0.974530	+	0.224258i	$0.0719958\pi$
$398$	−36.7658	−	15.2289i	−1.84290	−	0.763355i
$399$	−1.84136	+	1.84136i	−0.0921835	+	0.0921835i
$400$		0			0
$401$	−12.9334	−	5.35717i	−0.645861	−	0.267524i	0.0356143	−	0.999366i	$-0.488661\pi$
$401$	−12.9334	−	5.35717i	−0.645861	−	0.267524i	−0.681475	+	0.731841i	$0.738661\pi$
$402$	−5.14792	+	12.4282i	−0.256755	+	0.619861i
$403$	6.41345	−	2.65654i	0.319477	−	0.132332i
$404$			8.81465i			0.438545i
$405$		0			0
$406$	−0.113110	−	0.113110i	−0.00561357	−	0.00561357i
$407$	0.727259			0.0360489
$408$	−3.48876	−	2.24295i	−0.172719	−	0.111043i
$409$	−24.5879			−1.21579			−0.607896	−	0.794016i	$-0.707986\pi$
$409$	−24.5879			−1.21579			−0.607896	+	0.794016i	$0.707986\pi$
$410$		0			0
$411$	−3.56978	−	8.61821i	−0.176084	−	0.425105i
$412$		−	12.3980i		−	0.610807i
$413$	−8.79281	+	3.64210i	−0.432666	+	0.179216i
$414$	−10.4808	+	25.3030i	−0.515105	+	1.24357i
$415$		0			0
$416$	−10.8177	+	10.8177i	−0.530383	+	0.530383i
$417$	3.32019	−	3.32019i	0.162590	−	0.162590i
$418$	−0.515752	−	0.213632i	−0.0252263	−	0.0104491i
$419$	11.4857	−	27.7290i	0.561115	−	1.35465i	−0.347760	−	0.937583i	$-0.613058\pi$
$419$	11.4857	−	27.7290i	0.561115	−	1.35465i	0.908875	−	0.417068i	$-0.136942\pi$
$420$		0			0
$421$			2.84004i			0.138415i	0.997602	+	0.0692076i	$0.0220471\pi$
$421$			2.84004i			0.138415i	−0.997602	+	0.0692076i	$0.977953\pi$
$422$	−1.99015	−	4.80464i	−0.0968788	−	0.233886i
$423$	−15.5654	−	15.5654i	−0.756816	−	0.756816i
$424$	−6.87369			−0.333816
$425$		0			0
$426$	13.7740			0.667352
$427$	−0.211631	−	0.211631i	−0.0102415	−	0.0102415i
$428$	−7.80679	−	18.8472i	−0.377355	−	0.911016i
$429$		−	0.130928i		−	0.00632126i
$430$		0			0
$431$	2.29953	−	5.55155i	0.110764	−	0.267409i	−0.858771	−	0.512359i	$-0.828772\pi$
$431$	2.29953	−	5.55155i	0.110764	−	0.267409i	0.969536	+	0.244950i	$0.0787717\pi$
$432$	−15.5985	−	6.46109i	−0.750481	−	0.310860i
$433$	7.04962	−	7.04962i	0.338783	−	0.338783i	−0.517126	−	0.855909i	$-0.672998\pi$
$433$	7.04962	−	7.04962i	0.338783	−	0.338783i	0.855909	+	0.517126i	$0.172998\pi$
$434$	3.10380	−	3.10380i	0.148987	−	0.148987i
$435$		0			0
$436$	−1.01309	+	2.44582i	−0.0485183	+	0.117133i
$437$	23.0379	−	9.54262i	1.10205	−	0.456486i
$438$			6.83069i			0.326383i
$439$	0.481202	+	1.16173i	0.0229665	+	0.0554461i	0.934947	−	0.354788i	$-0.115447\pi$
$439$	0.481202	+	1.16173i	0.0229665	+	0.0554461i	−0.911980	+	0.410234i	$0.865447\pi$
$440$		0			0
$441$	−15.6449			−0.744995
$442$	−16.8792	+	11.7151i	−0.802861	+	0.557228i
$443$	−2.22305			−0.105620			−0.0528100	−	0.998605i	$-0.516818\pi$
$443$	−2.22305			−0.105620			−0.0528100	+	0.998605i	$0.516818\pi$
$444$	4.17016	+	4.17016i	0.197907	+	0.197907i
$445$		0			0
$446$		−	7.08691i		−	0.335575i
$447$	11.3845	−	4.71563i	0.538471	−	0.223042i
$448$	0.269285	−	0.650112i	0.0127225	−	0.0307149i
$449$	5.00234	+	2.07204i	0.236075	+	0.0977855i	0.497585	−	0.867415i	$-0.334220\pi$
$449$	5.00234	+	2.07204i	0.236075	+	0.0977855i	−0.261510	+	0.965201i	$0.584220\pi$
$450$		0			0
$451$	−0.453070	+	0.453070i	−0.0213343	+	0.0213343i
$452$	−0.843646	−	0.349449i	−0.0396818	−	0.0164367i
$453$	−3.31990	+	8.01495i	−0.155983	+	0.376575i
$454$	−13.3533	+	5.53114i	−0.626704	+	0.259589i
$455$		0			0
$456$	1.61312	+	3.89441i	0.0755412	+	0.182373i
$457$	0.754799	+	0.754799i	0.0353080	+	0.0353080i	0.724540	−	0.689232i	$-0.242052\pi$
$457$	0.754799	+	0.754799i	0.0353080	+	0.0353080i	−0.689232	+	0.724540i	$0.742052\pi$
$458$	7.56457			0.353469
$459$	−11.7141	−	7.53110i	−0.546768	−	0.351522i
$460$		0			0
$461$	20.9215	+	20.9215i	0.974413	+	0.974413i	0.999681	−	0.0252675i	$-0.00804376\pi$
$461$	20.9215	+	20.9215i	0.974413	+	0.974413i	−0.0252675	+	0.999681i	$0.508044\pi$
$462$	−0.0316813	−	0.0764855i	−0.00147395	−	0.00355843i
$463$		−	1.89160i		−	0.0879099i	−0.999034	−	0.0439549i	$-0.986004\pi$
$463$		−	1.89160i		−	0.0879099i	0.999034	−	0.0439549i	$-0.0139958\pi$
$464$	−0.408486	+	0.169200i	−0.0189635	+	0.00785494i
$465$		0			0
$466$	−0.0438989	−	0.0181835i	−0.00203358	−	0.000842335i
$467$	−12.2334	+	12.2334i	−0.566092	+	0.566092i	−0.931031	−	0.364939i	$-0.881090\pi$
$467$	−12.2334	+	12.2334i	−0.566092	+	0.566092i	0.364939	+	0.931031i	$0.381090\pi$
$468$	−5.53276	+	5.53276i	−0.255752	+	0.255752i
$469$	−12.3670	−	5.12256i	−0.571053	−	0.236538i
$470$		0			0
$471$	−6.43586	+	2.66582i	−0.296549	+	0.122835i
$472$			15.4058i			0.709109i
$473$	−0.0253499	−	0.0612000i	−0.00116559	−	0.00281398i
$474$	−7.69942	−	7.69942i	−0.353646	−	0.353646i
$475$		0			0
$476$	−2.39692	+	3.72824i	−0.109863	+	0.170884i
$477$	−10.8066			−0.494801
$478$	19.6299	+	19.6299i	0.897849	+	0.897849i
$479$	−9.92773	−	23.9676i	−0.453609	−	1.09511i	−0.970940	−	0.239324i	$-0.923074\pi$
$479$	−9.92773	−	23.9676i	−0.453609	−	1.09511i	0.517330	−	0.855786i	$-0.326926\pi$
$480$		0			0
$481$	−25.1331	+	10.4105i	−1.14597	+	0.474676i
$482$	9.52576	−	22.9972i	0.433886	−	1.04749i
$483$	3.41650	+	1.41516i	0.155456	+	0.0643921i
$484$	−8.05118	+	8.05118i	−0.365963	+	0.365963i
$485$		0			0
$486$	−21.9989	−	9.11225i	−0.997892	−	0.413340i
$487$	9.03010	−	21.8006i	0.409193	−	0.987879i	−0.576158	−	0.817339i	$-0.695449\pi$
$487$	9.03010	−	21.8006i	0.409193	−	0.987879i	0.985351	−	0.170541i	$-0.0545514\pi$
$488$	−0.447591	+	0.185398i	−0.0202615	+	0.00839258i
$489$			6.18892i			0.279873i
$490$		0			0
$491$	−13.2555	−	13.2555i	−0.598211	−	0.598211i	0.341626	−	0.939836i	$-0.389023\pi$
$491$	−13.2555	−	13.2555i	−0.598211	−	0.598211i	−0.939836	+	0.341626i	$0.889023\pi$
$492$	−5.19588			−0.234248
$493$	−0.356372	+	0.0774585i	−0.0160502	+	0.00348856i
$494$	20.8818			0.939515
$495$		0			0
$496$	−4.64294	−	11.2090i	−0.208474	−	0.503301i
$497$			13.7062i			0.614805i
$498$	9.35354	−	3.87436i	0.419142	−	0.173614i
$499$	−2.30180	+	5.55703i	−0.103043	+	0.248767i	−0.966990	−	0.254816i	$-0.917985\pi$
$499$	−2.30180	+	5.55703i	−0.103043	+	0.248767i	0.863947	+	0.503583i	$0.167985\pi$
$500$		0			0
$501$	−5.60557	+	5.60557i	−0.250438	+	0.250438i
$502$	−10.0559	+	10.0559i	−0.448815	+	0.448815i
$503$	−3.95467	−	1.63808i	−0.176330	−	0.0730382i	0.292772	−	0.956182i	$-0.405422\pi$
$503$	−3.95467	−	1.63808i	−0.176330	−	0.0730382i	−0.469102	+	0.883144i	$0.655422\pi$
$504$	1.76299	−	4.25624i	0.0785298	−	0.189588i
$505$		0			0
$506$			0.792752i			0.0352421i
$507$	−1.10426	−	2.66593i	−0.0490421	−	0.118398i
$508$	12.2912	+	12.2912i	0.545333	+	0.545333i
$509$	23.6694			1.04913			0.524563	−	0.851371i	$-0.324229\pi$
$509$	23.6694			1.04913			0.524563	+	0.851371i	$0.324229\pi$
$510$		0			0
$511$	−6.79705			−0.300684
$512$	7.02879	+	7.02879i	0.310632	+	0.310632i
$513$	5.41633	+	13.0762i	0.239137	+	0.577327i
$514$			17.0484i			0.751971i
$515$		0			0
$516$	0.205568	−	0.496284i	0.00904961	−	0.0218477i
$517$	−0.588670	−	0.243835i	−0.0258897	−	0.0107239i
$518$	−12.1632	+	12.1632i	−0.534420	+	0.534420i
$519$	9.55797	−	9.55797i	0.419548	−	0.419548i
$520$		0			0
$521$	5.50494	−	13.2901i	0.241176	−	0.582250i	−0.756224	−	0.654312i	$-0.772958\pi$
$521$	5.50494	−	13.2901i	0.241176	−	0.582250i	0.997400	+	0.0720626i	$0.0229581\pi$
$522$	−0.376101	+	0.155786i	−0.0164615	+	0.00681857i
$523$			21.3063i			0.931658i	0.884875	+	0.465829i	$0.154244\pi$
$523$			21.3063i			0.931658i	−0.884875	+	0.465829i	$0.845756\pi$
$524$	3.37031	+	8.13664i	0.147233	+	0.355451i
$525$		0			0
$526$	24.7672			1.07990
$527$	−2.12550	−	9.77900i	−0.0925881	−	0.425980i
$528$	−0.228828			−0.00995845
$529$	−8.77599	−	8.77599i	−0.381565	−	0.381565i
$530$		0			0
$531$			24.2206i			1.05108i
$532$	4.16174	−	1.72385i	0.180435	−	0.0747384i
$533$	9.17195	−	22.1430i	0.397281	−	0.959122i
$534$	0.102307	+	0.0423769i	0.00442725	+	0.00183383i
$535$		0			0
$536$	−15.3216	+	15.3216i	−0.661793	+	0.661793i
$537$	−2.95541	−	1.22417i	−0.127535	−	0.0528268i
$538$	15.1805	−	36.6489i	0.654477	−	1.58005i
$539$	−0.418378	+	0.173298i	−0.0180208	+	0.00746447i
$540$		0			0
$541$	−4.39065	−	10.6000i	−0.188769	−	0.455728i	0.800954	−	0.598726i	$-0.204326\pi$
$541$	−4.39065	−	10.6000i	−0.188769	−	0.455728i	−0.989723	+	0.142997i	$0.954326\pi$
$542$	−21.6862	−	21.6862i	−0.931502	−	0.931502i
$543$	−1.20812			−0.0518453
$544$	12.5749	+	18.1180i	0.539143	+	0.776804i
$545$		0			0
$546$	2.18973	+	2.18973i	0.0937117	+	0.0937117i
$547$	−6.34430	−	15.3165i	−0.271263	−	0.654886i	0.728275	−	0.685285i	$-0.240322\pi$
$547$	−6.34430	−	15.3165i	−0.271263	−	0.654886i	−0.999538	+	0.0303990i	$0.990322\pi$
$548$			16.1364i			0.689313i
$549$	−0.703690	+	0.291478i	−0.0300327	+	0.0124400i
$550$		0			0
$551$	0.342433	+	0.141841i	0.0145881	+	0.00604261i
$552$	4.23275	−	4.23275i	0.180158	−	0.180158i
$553$	7.66149	−	7.66149i	0.325800	−	0.325800i
$554$	−10.8433	−	4.49144i	−0.460687	−	0.190823i
$555$		0			0
$556$	−7.50410	+	3.10830i	−0.318245	+	0.131821i
$557$			31.0825i			1.31701i	0.752577	+	0.658504i	$0.228811\pi$
$557$			31.0825i			1.31701i	−0.752577	+	0.658504i	$0.771189\pi$
$558$	−4.27484	−	10.3204i	−0.180968	−	0.436896i
$559$	1.75211	+	1.75211i	0.0741065	+	0.0741065i
$560$		0			0
$561$	−0.185739	−	0.0335447i	−0.00784192	−	0.00141626i
$562$	40.0177			1.68805
$563$	3.78472	+	3.78472i	0.159507	+	0.159507i	0.782348	−	0.622841i	$-0.214022\pi$
$563$	3.78472	+	3.78472i	0.159507	+	0.159507i	−0.622841	+	0.782348i	$0.714022\pi$
$564$	−1.97731	−	4.77365i	−0.0832598	−	0.201007i
$565$		0			0
$566$	31.1786	−	12.9146i	1.31053	−	0.542841i
$567$	2.34459	−	5.66034i	0.0984635	−	0.237712i
$568$	20.4976	+	8.49038i	0.860060	+	0.356248i
$569$	10.5211	−	10.5211i	0.441066	−	0.441066i	−0.451304	−	0.892370i	$-0.649041\pi$
$569$	10.5211	−	10.5211i	0.441066	−	0.441066i	0.892370	+	0.451304i	$0.149041\pi$
$570$		0			0
$571$	39.2053	+	16.2393i	1.64069	+	0.679595i	0.996367	−	0.0851594i	$-0.0271399\pi$
$571$	39.2053	+	16.2393i	1.64069	+	0.679595i	0.644321	+	0.764755i	$0.277140\pi$
$572$	−0.0866717	+	0.209244i	−0.00362392	+	0.00874893i
$573$	7.12106	−	2.94964i	0.297486	−	0.123223i
$574$		−	15.1549i		−	0.632554i
$575$		0			0
$576$	−1.26628	−	1.26628i	−0.0527616	−	0.0527616i
$577$	41.2914			1.71898			0.859491	−	0.511151i	$-0.170781\pi$
$577$	41.2914			1.71898			0.859491	+	0.511151i	$0.170781\pi$
$578$	12.2949	+	26.9470i	0.511399	+	1.12085i
$579$	1.59096			0.0661181
$580$		0			0
$581$	3.85528	+	9.30747i	0.159944	+	0.386139i
$582$			8.93921i			0.370542i
$583$	−0.288992	+	0.119705i	−0.0119688	+	0.00495765i
$584$	−4.21048	+	10.1650i	−0.174231	+	0.420631i
$585$		0			0
$586$	24.8982	−	24.8982i	1.02853	−	1.02853i
$587$	−12.1282	+	12.1282i	−0.500586	+	0.500586i	−0.911620	−	0.411034i	$-0.865168\pi$
$587$	−12.1282	+	12.1282i	−0.500586	+	0.500586i	0.411034	+	0.911620i	$0.365168\pi$
$588$	−3.39272	−	1.40531i	−0.139913	−	0.0579540i
$589$	−3.89217	+	9.39652i	−0.160374	+	0.387177i
$590$		0			0
$591$		−	10.3721i		−	0.426650i
$592$	18.1948	+	43.9261i	0.747801	+	1.80535i
$593$	−22.6078	−	22.6078i	−0.928392	−	0.928392i	0.0692104	−	0.997602i	$-0.477952\pi$
$593$	−22.6078	−	22.6078i	−0.928392	−	0.928392i	−0.997602	+	0.0692104i	$0.977952\pi$
$594$	−0.449960			−0.0184621
$595$		0			0
$596$	−21.3160			−0.873138
$597$	9.66930	+	9.66930i	0.395738	+	0.395738i
$598$	−11.3480	−	27.3964i	−0.464053	−	1.12032i
$599$		−	18.5632i		−	0.758473i	−0.925300	−	0.379237i	$-0.876187\pi$
$599$		−	18.5632i		−	0.758473i	0.925300	−	0.379237i	$-0.123813\pi$
$600$		0			0
$601$	8.19864	−	19.7933i	0.334430	−	0.807384i	−0.663800	−	0.747910i	$-0.731058\pi$
$601$	8.19864	−	19.7933i	0.334430	−	0.807384i	0.998230	−	0.0594745i	$-0.0189425\pi$
$602$	1.44752	+	0.599583i	0.0589965	+	0.0244372i
$603$	−24.0882	+	24.0882i	−0.980948	+	0.980948i
$604$	10.6115	−	10.6115i	0.431775	−	0.431775i
$605$		0			0
$606$	3.39754	−	8.20240i	0.138016	−	0.333200i
$607$	3.29333	−	1.36414i	0.133672	−	0.0553688i	−0.314845	−	0.949143i	$-0.601952\pi$
$607$	3.29333	−	1.36414i	0.133672	−	0.0553688i	0.448517	+	0.893774i	$0.351952\pi$
$608$		−	22.4144i		−	0.909023i
$609$	0.0210348	+	0.0507825i	0.000852373	+	0.00205781i
$610$		0			0
$611$	23.8340			0.964222
$612$	6.43145	+	9.26652i	0.259976	+	0.374577i
$613$	−19.4457			−0.785402			−0.392701	−	0.919666i	$-0.628459\pi$
$613$	−19.4457			−0.785402			−0.392701	+	0.919666i	$0.628459\pi$
$614$	−22.2788	−	22.2788i	−0.899101	−	0.899101i
$615$		0			0
$616$		−	0.133349i		−	0.00537280i
$617$	6.54562	−	2.71129i	0.263517	−	0.109152i	−0.247013	−	0.969012i	$-0.579449\pi$
$617$	6.54562	−	2.71129i	0.263517	−	0.109152i	0.510530	+	0.859860i	$0.329449\pi$
$618$	−4.77874	+	11.5369i	−0.192229	+	0.464082i
$619$	−7.48218	−	3.09922i	−0.300734	−	0.124568i	0.227214	−	0.973845i	$-0.427038\pi$
$619$	−7.48218	−	3.09922i	−0.300734	−	0.124568i	−0.527948	+	0.849277i	$0.677038\pi$
$620$		0			0
$621$	14.2122	−	14.2122i	0.570316	−	0.570316i
$622$	32.9260	+	13.6384i	1.32021	+	0.546850i
$623$	−0.0421682	+	0.101803i	−0.00168943	+	0.00407865i
$624$	7.90798	−	3.27559i	0.316572	−	0.131129i
$625$		0			0
$626$	15.8625	+	38.2955i	0.633994	+	1.53060i
$627$	0.135641	+	0.135641i	0.00541700	+	0.00541700i
$628$	12.0503			0.480858
$629$	8.32941	+	38.3220i	0.332116	+	1.52800i
$630$		0			0
$631$	−5.93919	−	5.93919i	−0.236436	−	0.236436i	0.578937	−	0.815372i	$-0.303468\pi$
$631$	−5.93919	−	5.93919i	−0.236436	−	0.236436i	−0.815372	+	0.578937i	$0.803468\pi$
$632$	−6.71181	−	16.2038i	−0.266982	−	0.644551i
$633$			1.78701i			0.0710273i
$634$	8.42116	−	3.48816i	0.334447	−	0.138533i
$635$		0			0
$636$	−2.34350	−	0.970709i	−0.0929258	−	0.0384911i
$637$	11.9779	−	11.9779i	0.474581	−	0.474581i
$638$	−0.00833211	+	0.00833211i	−0.000329871	+	0.000329871i
$639$	32.2257	+	13.3483i	1.27483	+	0.528052i
$640$		0			0
$641$	−1.23638	+	0.512124i	−0.0488340	+	0.0202277i	−0.406967	−	0.913443i	$-0.633414\pi$
$641$	−1.23638	+	0.512124i	−0.0488340	+	0.0202277i	0.358133	+	0.933671i	$0.383414\pi$
$642$			20.5472i			0.810934i
$643$	16.7357	+	40.4035i	0.659991	+	1.59336i	0.797815	+	0.602902i	$0.205989\pi$
$643$	16.7357	+	40.4035i	0.659991	+	1.59336i	−0.137825	+	0.990457i	$0.544011\pi$
$644$	−4.52331	−	4.52331i	−0.178243	−	0.178243i
$645$		0			0
$646$	5.35006	−	29.6237i	0.210495	−	1.16553i
$647$	−25.4968			−1.00238			−0.501191	−	0.865337i	$-0.667105\pi$
$647$	−25.4968			−1.00238			−0.501191	+	0.865337i	$0.667105\pi$
$648$	−7.01268	−	7.01268i	−0.275484	−	0.275484i
$649$	0.268290	+	0.647710i	0.0105313	+	0.0254248i
$650$		0			0
$651$	−1.39349	+	0.577204i	−0.0546153	+	0.0226224i
$652$	4.09694	−	9.89090i	0.160449	−	0.387357i
$653$	7.60853	+	3.15156i	0.297745	+	0.123330i	0.526555	−	0.850141i	$-0.323483\pi$
$653$	7.60853	+	3.15156i	0.297745	+	0.123330i	−0.228810	+	0.973471i	$0.573483\pi$
$654$	1.88545	−	1.88545i	0.0737268	−	0.0737268i
$655$		0			0
$656$	−38.7003	−	16.0302i	−1.51099	−	0.625873i
$657$	−6.61960	+	15.9811i	−0.258255	+	0.623483i
$658$	13.9234	−	5.76726i	0.542790	−	0.224831i
$659$			30.4524i			1.18626i	0.805108	+	0.593129i	$0.202107\pi$
$659$			30.4524i			1.18626i	−0.805108	+	0.593129i	$0.797893\pi$
$660$		0			0
$661$	13.8024	+	13.8024i	0.536850	+	0.536850i	0.922602	−	0.385752i	$-0.126058\pi$
$661$	13.8024	+	13.8024i	0.536850	+	0.536850i	−0.385752	+	0.922602i	$0.626058\pi$
$662$	43.9844			1.70950
$663$	6.89908	−	1.49954i	0.267938	−	0.0582372i
$664$	16.3075			0.632855
$665$		0			0
$666$	16.7523	+	40.4436i	0.649137	+	1.56716i
$667$		−	0.526347i		−	0.0203802i
$668$	12.6694	−	5.24783i	0.490193	−	0.203045i
$669$	−0.931919	+	2.24985i	−0.0360301	+	0.0869842i
$670$		0			0
$671$	−0.0155895	+	0.0155895i	−0.000601826	+	0.000601826i
$672$	2.35044	−	2.35044i	0.0906703	−	0.0906703i
$673$	−28.1304	−	11.6520i	−1.08435	−	0.449151i	−0.232314	−	0.972641i	$-0.574630\pi$
$673$	−28.1304	−	11.6520i	−1.08435	−	0.449151i	−0.852032	+	0.523490i	$0.824630\pi$
$674$	−0.395754	+	0.955435i	−0.0152439	+	0.0368020i
$675$		0			0
$676$			4.99159i			0.191984i
$677$	16.7122	+	40.3468i	0.642302	+	1.55066i	0.823566	+	0.567220i	$0.191981\pi$
$677$	16.7122	+	40.3468i	0.642302	+	1.55066i	−0.181264	+	0.983435i	$0.558019\pi$
$678$	0.650355	+	0.650355i	0.0249767	+	0.0249767i
$679$	−8.89518			−0.341366
$680$		0			0
$681$	4.96657			0.190319
$682$	−0.228637	−	0.228637i	−0.00875495	−	0.00875495i
$683$	16.1714	+	39.0413i	0.618783	+	1.49387i	0.853118	+	0.521719i	$0.174709\pi$
$683$	16.1714	+	39.0413i	0.618783	+	1.49387i	−0.234334	+	0.972156i	$0.575291\pi$
$684$		−	11.4639i		−	0.438333i
$685$		0			0
$686$	8.94343	−	21.5914i	0.341462	−	0.824362i
$687$	−2.40149	−	0.994730i	−0.0916226	−	0.0379513i
$688$	3.06224	−	3.06224i	0.116747	−	0.116747i
$689$	8.27365	−	8.27365i	0.315201	−	0.315201i
$690$		0			0
$691$	0.281277	−	0.679063i	0.0107003	−	0.0258328i	−0.918439	−	0.395562i	$-0.870550\pi$
$691$	0.281277	−	0.679063i	0.0107003	−	0.0258328i	0.929139	+	0.369730i	$0.120550\pi$
$692$	−21.6024	+	8.94799i	−0.821199	+	0.340152i
$693$		−	0.209648i		−	0.00796388i
$694$	−1.35624	−	3.27426i	−0.0514822	−	0.124289i
$695$		0			0
$696$	0.0889755			0.00337261
$697$	−29.0631	−	18.6849i	−1.10084	−	0.707741i
$698$	−5.15797			−0.195232
$699$	0.0115453	+	0.0115453i	0.000436683	+	0.000436683i
$700$		0			0
$701$		−	14.1492i		−	0.534409i	−0.963640	−	0.267204i	$-0.913900\pi$
$701$		−	14.1492i		−	0.534409i	0.963640	−	0.267204i	$-0.0860999\pi$
$702$	15.5500	−	6.44103i	0.586898	−	0.243101i
$703$	15.2527	−	36.8232i	0.575265	−	1.38881i
$704$	−0.0478896	−	0.0198365i	−0.00180491	−	0.000747616i
$705$		0			0
$706$	−19.7829	+	19.7829i	−0.744539	+	0.744539i
$707$	8.16200	+	3.38081i	0.306964	+	0.127148i
$708$	−2.17562	+	5.25242i	−0.0817649	+	0.197398i
$709$	25.8317	−	10.6998i	0.970129	−	0.401841i	0.159369	−	0.987219i	$-0.449054\pi$
$709$	25.8317	−	10.6998i	0.970129	−	0.401841i	0.810760	+	0.585378i	$0.199054\pi$
$710$		0			0
$711$	−10.5521	−	25.4751i	−0.395736	−	0.955390i
$712$	0.126125	+	0.126125i	0.00472675	+	0.00472675i
$713$	14.4432			0.540902
$714$	3.66746	−	2.54541i	0.137251	−	0.0952596i
$715$		0			0
$716$	3.91284	+	3.91284i	0.146230	+	0.146230i
$717$	−3.65051	−	8.81311i	−0.136331	−	0.329132i
$718$			35.3328i			1.31861i
$719$	−38.3914	+	15.9022i	−1.43176	+	0.593054i	−0.957785	−	0.287485i	$-0.907181\pi$
$719$	−38.3914	+	15.9022i	−1.43176	+	0.593054i	−0.473974	+	0.880539i	$0.657181\pi$
$720$		0			0
$721$	−11.4801	−	4.75520i	−0.427540	−	0.177093i
$722$	1.77447	−	1.77447i	0.0660391	−	0.0660391i
$723$	−6.04821	+	6.04821i	−0.224935	+	0.224935i
$724$	1.93077	+	0.799750i	0.0717564	+	0.0297225i
$725$		0			0
$726$	10.5952	−	4.38869i	0.393226	−	0.162879i
$727$			25.9162i			0.961177i	0.876946	+	0.480589i	$0.159577\pi$
$727$			25.9162i			0.961177i	−0.876946	+	0.480589i	$0.840423\pi$
$728$	1.90885	+	4.60838i	0.0707468	+	0.170798i
$729$	−6.73550	−	6.73550i	−0.249463	−	0.249463i
$730$		0			0
$731$	2.93452	−	2.03671i	0.108537	−	0.0753306i
$732$	−0.178783			−0.00660800
$733$	−2.02367	−	2.02367i	−0.0747458	−	0.0747458i	0.668746	−	0.743491i	$-0.266832\pi$
$733$	−2.02367	−	2.02367i	−0.0747458	−	0.0747458i	−0.743491	+	0.668746i	$0.766832\pi$
$734$	−13.7105	−	33.1001i	−0.506064	−	1.22175i
$735$		0			0
$736$	−29.4072	+	12.1809i	−1.08396	+	0.448992i
$737$	−0.377346	+	0.910995i	−0.0138997	+	0.0335569i
$738$	−35.6321	−	14.7593i	−1.31163	−	0.543297i
$739$	−20.3671	+	20.3671i	−0.749214	+	0.749214i	−0.974332	−	0.225118i	$-0.927723\pi$
$739$	−20.3671	+	20.3671i	−0.749214	+	0.749214i	0.225118	+	0.974332i	$0.427723\pi$
$740$		0			0
$741$	−6.62924	−	2.74592i	−0.243531	−	0.100874i
$742$	2.83129	−	6.83533i	0.103940	−	0.250933i
$743$	13.1194	−	5.43425i	0.481306	−	0.199363i	−0.128820	−	0.991668i	$-0.541119\pi$
$743$	13.1194	−	5.43425i	0.481306	−	0.199363i	0.610126	+	0.792305i	$0.291119\pi$
$744$			2.44153i			0.0895107i
$745$		0			0
$746$	−6.69235	−	6.69235i	−0.245024	−	0.245024i
$747$	25.6382			0.938054
$748$	0.274636	+	0.176566i	0.0100417	+	0.00645588i
$749$	−20.4460			−0.747081
$750$		0			0
$751$	17.9916	+	43.4356i	0.656523	+	1.58499i	0.803138	+	0.595793i	$0.203162\pi$
$751$	17.9916	+	43.4356i	0.656523	+	1.58499i	−0.146615	+	0.989194i	$0.546838\pi$
$752$		−	41.6557i		−	1.51903i
$753$	4.51472	−	1.87006i	0.164526	−	0.0681488i
$754$	0.168675	−	0.407218i	0.00614278	−	0.0148300i
$755$		0			0
$756$	2.56740	−	2.56740i	0.0933754	−	0.0933754i
$757$	−9.35712	+	9.35712i	−0.340090	+	0.340090i	−0.856401	−	0.516311i	$-0.827305\pi$
$757$	−9.35712	+	9.35712i	−0.340090	+	0.340090i	0.516311	+	0.856401i	$0.327305\pi$
$758$	31.4815	+	13.0401i	1.14346	+	0.473637i
$759$	0.104246	−	0.251672i	0.00378388	−	0.00913510i
$760$		0			0
$761$			29.0026i			1.05134i	0.850688	+	0.525672i	$0.176186\pi$
$761$			29.0026i			1.05134i	−0.850688	+	0.525672i	$0.823814\pi$
$762$	−6.69990	−	16.1750i	−0.242712	−	0.585958i
$763$	1.87616	+	1.87616i	0.0679216	+	0.0679216i
$764$	−13.3332			−0.482378
$765$		0			0
$766$	19.2081			0.694015
$767$	−18.5435	−	18.5435i	−0.669566	−	0.669566i
$768$	−4.43128	−	10.6981i	−0.159900	−	0.386033i
$769$			32.5187i			1.17265i	0.810075	+	0.586327i	$0.199427\pi$
$769$			32.5187i			1.17265i	−0.810075	+	0.586327i	$0.800573\pi$
$770$		0			0
$771$	2.24184	−	5.41227i	0.0807378	−	0.194918i
$772$	−2.54261	−	1.05318i	−0.0915107	−	0.0379050i
$773$	−13.7423	+	13.7423i	−0.494275	+	0.494275i	−0.909650	−	0.415375i	$-0.863650\pi$
$773$	−13.7423	+	13.7423i	−0.494275	+	0.494275i	0.415375	+	0.909650i	$0.363650\pi$
$774$	2.81946	−	2.81946i	0.101343	−	0.101343i
$775$		0			0
$776$	−5.51018	+	13.3028i	−0.197804	+	0.477541i
$777$	5.46084	−	2.26195i	0.195906	−	0.0811471i
$778$		−	18.7693i		−	0.672912i
$779$	13.4381	+	32.4424i	0.481469	+	1.16237i
$780$		0			0
$781$	1.00964			0.0361279
$782$	−41.7731	+	9.07951i	−1.49380	+	0.324683i
$783$	0.298751			0.0106765
$784$	−20.9342	−	20.9342i	−0.747651	−	0.747651i
$785$		0			0
$786$		−	8.87055i		−	0.316402i
$787$	17.2673	−	7.15233i	0.615511	−	0.254953i	−0.0530716	−	0.998591i	$-0.516901\pi$
$787$	17.2673	−	7.15233i	0.615511	−	0.254953i	0.668583	+	0.743638i	$0.266901\pi$
$788$	−6.86610	+	16.5762i	−0.244595	+	0.590504i
$789$	−7.86274	−	3.25685i	−0.279921	−	0.115947i
$790$		0			0
$791$	−0.647151	+	0.647151i	−0.0230101	+	0.0230101i
$792$	−0.313530	−	0.129868i	−0.0111408	−	0.00461466i
$793$	0.315593	−	0.761910i	0.0112070	−	0.0270562i
$794$	10.6321	−	4.40395i	0.377318	−	0.156290i
$795$		0			0
$796$	−9.05222	−	21.8540i	−0.320847	−	0.774594i
$797$	−10.2971	−	10.2971i	−0.364743	−	0.364743i	0.500813	−	0.865556i	$-0.333034\pi$
$797$	−10.2971	−	10.2971i	−0.364743	−	0.364743i	−0.865556	+	0.500813i	$0.833034\pi$
$798$	−4.53712			−0.160612
$799$	6.10646	−	33.8119i	0.216031	−	1.19618i
$800$		0			0
$801$	0.198291	+	0.198291i	0.00700625	+	0.00700625i
$802$	−9.33386	−	22.5339i	−0.329590	−	0.795701i
$803$			0.500695i			0.0176691i
$804$	−7.38745	+	3.05998i	−0.260535	+	0.107917i
$805$		0			0
$806$	11.1742	+	4.62852i	0.393595	+	0.163033i
$807$	−9.63856	+	9.63856i	−0.339293	+	0.339293i
$808$	10.1120	−	10.1120i	0.355740	−	0.355740i
$809$	18.7042	+	7.74755i	0.657606	+	0.272389i	0.686431	−	0.727195i	$-0.259176\pi$
$809$	18.7042	+	7.74755i	0.657606	+	0.272389i	−0.0288248	+	0.999584i	$0.509176\pi$
$810$		0			0
$811$	−36.4099	+	15.0815i	−1.27852	+	0.529582i	−0.915545	−	0.402215i	$-0.868240\pi$
$811$	−36.4099	+	15.0815i	−1.27852	+	0.529582i	−0.362979	+	0.931797i	$0.618240\pi$
$812$		−	0.0950833i		−	0.00333677i
$813$	4.03292	+	9.73633i	0.141441	+	0.341468i
$814$	0.895984	+	0.895984i	0.0314042	+	0.0314042i
$815$		0			0
$816$	−2.62080	−	12.0578i	−0.0917464	−	0.422107i
$817$	−3.63039			−0.127011
$818$	−30.2923	−	30.2923i	−1.05914	−	1.05914i
$819$	3.00104	+	7.24516i	0.104865	+	0.253166i
$820$		0			0
$821$	−17.2968	+	7.16455i	−0.603661	+	0.250045i	−0.663516	−	0.748163i	$-0.730936\pi$
$821$	−17.2968	+	7.16455i	−0.603661	+	0.250045i	0.0598545	+	0.998207i	$0.480936\pi$
$822$	6.21966	−	15.0156i	0.216936	−	0.523729i
$823$	46.6517	+	19.3237i	1.62617	+	0.673583i	0.994796	−	0.101891i	$-0.0324893\pi$
$823$	46.6517	+	19.3237i	1.62617	+	0.673583i	0.631379	+	0.775475i	$0.282489\pi$
$824$	−14.2228	+	14.2228i	−0.495476	+	0.495476i
$825$		0			0
$826$	−15.3198	−	6.34568i	−0.533045	−	0.220794i
$827$	−11.5136	+	27.7963i	−0.400367	+	0.966571i	0.587210	+	0.809434i	$0.300226\pi$
$827$	−11.5136	+	27.7963i	−0.400367	+	0.966571i	−0.987577	+	0.157136i	$0.949774\pi$
$828$	−15.0404	+	6.22993i	−0.522689	+	0.216505i
$829$		−	15.6619i		−	0.543959i	−0.962303	−	0.271980i	$-0.912322\pi$
$829$		−	15.6619i		−	0.543959i	0.962303	−	0.271980i	$-0.0876784\pi$
$830$		0			0
$831$	2.85175	+	2.85175i	0.0989263	+	0.0989263i
$832$	1.93895			0.0672210
$833$	−13.9235	−	20.0611i	−0.482420	−	0.695077i
$834$	8.18095			0.283283
$835$		0			0
$836$	−0.126985	−	0.306569i	−0.00439187	−	0.0106029i
$837$			8.19785i			0.283359i
$838$	48.3126	−	20.0117i	1.66893	−	0.691294i
$839$	−5.46594	+	13.1959i	−0.188705	+	0.455575i	−0.989711	−	0.143082i	$-0.954299\pi$
$839$	−5.46594	+	13.1959i	−0.188705	+	0.455575i	0.801006	+	0.598657i	$0.204299\pi$
$840$		0			0
$841$	−20.5006	+	20.5006i	−0.706916	+	0.706916i
$842$	−3.49894	+	3.49894i	−0.120581	+	0.120581i
$843$	−12.7043	−	5.26228i	−0.437558	−	0.181242i
$844$	1.18297	−	2.85593i	0.0407193	−	0.0983052i
$845$		0			0
$846$		−	38.3532i		−	1.31861i
$847$	4.36707	+	10.5430i	0.150054	+	0.362263i
$848$	−14.4602	−	14.4602i	−0.496565	−	0.496565i
$849$	−11.5964			−0.397987
$850$		0			0
$851$	−56.6001			−1.94023
$852$	5.78938	+	5.78938i	0.198341	+	0.198341i
$853$	−9.54040	−	23.0326i	−0.326657	−	0.788620i	−0.998836	−	0.0482315i	$-0.984641\pi$
$853$	−9.54040	−	23.0326i	−0.326657	−	0.788620i	0.672179	−	0.740389i	$-0.265359\pi$
$854$		−	0.521459i		−	0.0178440i
$855$		0			0
$856$	−12.6654	+	30.5771i	−0.432896	+	1.04510i
$857$	−6.35764	−	2.63342i	−0.217173	−	0.0899559i	0.271445	−	0.962454i	$-0.412499\pi$
$857$	−6.35764	−	2.63342i	−0.217173	−	0.0899559i	−0.488617	+	0.872498i	$0.662499\pi$
$858$	0.161303	−	0.161303i	0.00550680	−	0.00550680i
$859$	28.0355	−	28.0355i	0.956560	−	0.956560i	−0.0425346	−	0.999095i	$-0.513543\pi$
$859$	28.0355	−	28.0355i	0.956560	−	0.956560i	0.999095	+	0.0425346i	$0.0135433\pi$
$860$		0			0
$861$	−1.99285	+	4.81117i	−0.0679162	+	0.163964i
$862$	9.67253	−	4.00649i	0.329448	−	0.136462i
$863$			11.0858i			0.377364i	0.982038	+	0.188682i	$0.0604216\pi$
$863$			11.0858i			0.377364i	−0.982038	+	0.188682i	$0.939578\pi$
$864$	−6.91376	−	16.6913i	−0.235211	−	0.567850i
$865$		0			0
$866$	17.3703			0.590266
$867$	−0.359708	−	10.1715i	−0.0122163	−	0.345442i
$868$	2.60913			0.0885595
$869$	−0.564373	−	0.564373i	−0.0191450	−	0.0191450i
$870$		0			0
$871$		−	36.8843i		−	1.24978i
$872$	3.96800	−	1.64360i	0.134374	−	0.0556594i
$873$	−8.66296	+	20.9142i	−0.293197	+	0.707839i
$874$	40.1393	+	16.6262i	1.35773	+	0.562390i
$875$		0			0
$876$	−2.87102	+	2.87102i	−0.0970029	+	0.0970029i
$877$	−35.2441	−	14.5986i	−1.19011	−	0.492959i	−0.302318	−	0.953207i	$-0.597760\pi$
$877$	−35.2441	−	14.5986i	−1.19011	−	0.492959i	−0.887790	+	0.460248i	$0.847760\pi$
$878$	−0.838404	+	2.02409i	−0.0282948	+	0.0683096i
$879$	−11.1784	+	4.63024i	−0.377038	+	0.156174i
$880$		0			0
$881$	−1.47285	−	3.55578i	−0.0496216	−	0.119797i	0.897125	−	0.441777i	$-0.145652\pi$
$881$	−1.47285	−	3.55578i	−0.0496216	−	0.119797i	−0.946747	+	0.321980i	$0.895652\pi$
$882$	−19.2745	−	19.2745i	−0.649007	−	0.649007i
$883$	−44.4321			−1.49526			−0.747629	−	0.664116i	$-0.768808\pi$
$883$	−44.4321			−1.49526			−0.747629	+	0.664116i	$0.768808\pi$
$884$	−12.0185	−	2.17055i	−0.404226	−	0.0730036i
$885$		0			0
$886$	−2.73879	−	2.73879i	−0.0920115	−	0.0920115i
$887$	1.07118	+	2.58606i	0.0359667	+	0.0868314i	0.940842	−	0.338845i	$-0.110036\pi$
$887$	1.07118	+	2.58606i	0.0359667	+	0.0868314i	−0.904875	+	0.425676i	$0.860036\pi$
$888$		−	9.56788i		−	0.321077i
$889$	16.0953	−	6.66691i	0.539820	−	0.223601i
$890$		0			0
$891$	−0.416961	−	0.172711i	−0.0139687	−	0.00578603i
$892$	2.97871	−	2.97871i	0.0997347	−	0.0997347i
$893$	−24.6921	+	24.6921i	−0.826290	+	0.826290i
$894$	19.8354	+	8.21610i	0.663396	+	0.274788i
$895$		0			0
$896$	11.3916	−	4.71857i	0.380568	−	0.157636i
$897$			10.1897i			0.340223i
$898$	3.61014	+	8.71564i	0.120472	+	0.290845i
$899$	0.151803	+	0.151803i	0.00506292	+	0.00506292i
$900$		0			0
$901$	−9.61755	−	13.8571i	−0.320407	−	0.461647i
$902$	−1.11637			−0.0371709
$903$	−0.380694	−	0.380694i	−0.0126687	−	0.0126687i
$904$	0.566934	+	1.36870i	0.0188559	+	0.0455223i
$905$		0			0
$906$	−13.9645	+	5.78430i	−0.463941	+	0.192171i
$907$	15.4777	−	37.3664i	0.513928	−	1.24073i	−0.427653	−	0.903943i	$-0.640659\pi$
$907$	15.4777	−	37.3664i	0.513928	−	1.24073i	0.941580	−	0.336788i	$-0.109341\pi$
$908$	−7.93738	−	3.28777i	−0.263411	−	0.109108i
$909$	15.8978	−	15.8978i	0.527298	−	0.527298i
$910$		0			0
$911$	31.3733	+	12.9953i	1.03944	+	0.430552i	0.836113	−	0.548558i	$-0.184823\pi$
$911$	31.3733	+	12.9953i	1.03944	+	0.430552i	0.203332	+	0.979110i	$0.434823\pi$
$912$	−4.79916	+	11.5862i	−0.158916	+	0.383657i
$913$	0.685622	−	0.283994i	0.0226908	−	0.00939882i
$914$			1.85982i			0.0615175i
$915$		0			0
$916$	3.17948	+	3.17948i	0.105053	+	0.105053i
$917$	8.82686			0.291489
$918$	−5.15347	−	23.7101i	−0.170090	−	0.782550i
$919$	−17.7466			−0.585407			−0.292703	−	0.956203i	$-0.594555\pi$
$919$	−17.7466			−0.585407			−0.292703	+	0.956203i	$0.594555\pi$
$920$		0			0
$921$	4.14313	+	10.0024i	0.136521	+	0.329591i
$922$			51.5507i			1.69773i
$923$	−34.8919	+	14.4527i	−1.14848	+	0.475717i
$924$	0.0188317	−	0.0454639i	0.000619519	−	0.00149565i
$925$		0			0
$926$	2.33045	−	2.33045i	0.0765832	−	0.0765832i
$927$	−22.3607	+	22.3607i	−0.734422	+	0.734422i
$928$	−0.437105	−	0.181055i	−0.0143487	−	0.00594342i
$929$	−21.2208	+	51.2316i	−0.696233	+	1.68085i	0.0355957	+	0.999366i	$0.488667\pi$
$929$	−21.2208	+	51.2316i	−0.696233	+	1.68085i	−0.731829	+	0.681489i	$0.761333\pi$
$930$		0			0
$931$			24.8182i			0.813384i
$932$	−0.0108085	−	0.0260940i	−0.000354044	−	0.000854737i
$933$	−8.65945	−	8.65945i	−0.283498	−	0.283498i
$934$	−30.1430			−0.986309
$935$		0			0
$936$	12.6942			0.414922
$937$	−17.0689	−	17.0689i	−0.557618	−	0.557618i	0.371010	−	0.928629i	$-0.379011\pi$
$937$	−17.0689	−	17.0689i	−0.557618	−	0.557618i	−0.928629	+	0.371010i	$0.879011\pi$
$938$	−8.92510	−	21.5471i	−0.291415	−	0.703538i
$939$		−	14.2434i		−	0.464817i
$940$		0			0
$941$	13.0818	−	31.5822i	0.426453	−	1.02955i	−0.553950	−	0.832550i	$-0.686880\pi$
$941$	13.0818	−	31.5822i	0.426453	−	1.02955i	0.980404	−	0.197000i	$-0.0631198\pi$
$942$	−11.2133	−	4.64469i	−0.365348	−	0.151332i
$943$	35.2609	−	35.2609i	1.14825	−	1.14825i
$944$	−32.4092	+	32.4092i	−1.05483	+	1.05483i
$945$		0			0
$946$	0.0441674	−	0.106630i	0.00143601	−	0.00346682i
$947$	14.6757	−	6.07889i	0.476897	−	0.197537i	−0.131269	−	0.991347i	$-0.541905\pi$
$947$	14.6757	−	6.07889i	0.476897	−	0.197537i	0.608167	+	0.793809i	$0.291905\pi$
$948$		−	6.47232i		−	0.210211i
$949$	−7.16728	−	17.3033i	−0.232660	−	0.561690i
$950$		0			0
$951$	−3.13212			−0.101566
$952$	7.02669	−	1.52727i	0.227736	−	0.0494992i
$953$	−2.52080			−0.0816568			−0.0408284	−	0.999166i	$-0.513000\pi$
$953$	−2.52080			−0.0816568			−0.0408284	+	0.999166i	$0.513000\pi$
$954$	−13.3138	−	13.3138i	−0.431049	−	0.431049i
$955$		0			0
$956$			16.5013i			0.533691i
$957$	0.00374082	−	0.00154950i	0.000120924	−	5.00882e-5i
$958$	17.2972	−	41.7591i	0.558847	−	1.34918i
$959$	14.9416	+	6.18903i	0.482491	+	0.199854i
$960$		0			0
$961$	17.7548	−	17.7548i	0.572734	−	0.572734i
$962$	−43.7897	−	18.1383i	−1.41184	−	0.584801i
$963$	−19.9122	+	48.0724i	−0.641663	+	1.54911i
$964$	13.6698	−	5.66222i	0.440275	−	0.182368i
$965$		0			0
$966$	2.46565	+	5.95261i	0.0793310	+	0.191522i
$967$	−21.6277	−	21.6277i	−0.695499	−	0.695499i	0.267938	−	0.963436i	$-0.413658\pi$
$967$	−21.6277	−	21.6277i	−0.695499	−	0.695499i	−0.963436	+	0.267938i	$0.913658\pi$
$968$	18.4724			0.593724
$969$	−5.59393	+	8.70098i	−0.179703	+	0.279516i
$970$		0			0
$971$	19.9547	+	19.9547i	0.640376	+	0.640376i	0.950648	−	0.310272i	$-0.100420\pi$
$971$	19.9547	+	19.9547i	0.640376	+	0.640376i	−0.310272	+	0.950648i	$0.600420\pi$
$972$	−5.41643	−	13.0764i	−0.173732	−	0.419426i
$973$			8.14066i			0.260978i
$974$	37.9834	−	15.7332i	1.21707	−	0.504126i
$975$		0			0
$976$	−1.33162	−	0.551575i	−0.0426241	−	0.0176555i
$977$	−27.0094	+	27.0094i	−0.864109	+	0.864109i	−0.991812	−	0.127704i	$-0.959239\pi$
$977$	−27.0094	+	27.0094i	−0.864109	+	0.864109i	0.127704	+	0.991812i	$0.459239\pi$
$978$	−7.62475	+	7.62475i	−0.243813	+	0.243813i
$979$	0.00749918	+	0.00310626i	0.000239675	+	9.92765e-5i
$980$		0			0
$981$	6.23838	−	2.58402i	0.199176	−	0.0825015i
$982$		−	32.6615i		−	1.04227i
$983$	1.56112	+	3.76887i	0.0497919	+	0.120208i	0.946818	−	0.321769i	$-0.104277\pi$
$983$	1.56112	+	3.76887i	0.0497919	+	0.120208i	−0.897026	+	0.441977i	$0.854277\pi$
$984$	5.96063	+	5.96063i	0.190018	+	0.190018i
$985$		0			0
$986$	−0.534479	−	0.343621i	−0.0170213	−	0.0109431i
$987$	−5.17859			−0.164836
$988$	8.77686	+	8.77686i	0.279229	+	0.279229i
$989$	1.97290	+	4.76299i	0.0627344	+	0.151454i
$990$		0			0
$991$	41.6209	−	17.2400i	1.32213	−	0.547645i	0.393732	−	0.919225i	$-0.371184\pi$
$991$	41.6209	−	17.2400i	1.32213	−	0.547645i	0.928401	+	0.371580i	$0.121184\pi$
$992$	4.96822	−	11.9944i	0.157741	−	0.380821i
$993$	−13.9635	−	5.78388i	−0.443119	−	0.183546i
$994$	−16.8860	+	16.8860i	−0.535591	+	0.535591i
$995$		0			0
$996$	5.55985	+	2.30297i	0.176171	+	0.0729723i
$997$	9.47110	−	22.8653i	0.299953	−	0.724150i	−0.699997	−	0.714146i	$-0.746815\pi$
$997$	9.47110	−	22.8653i	0.299953	−	0.724150i	0.999950	−	0.0100043i	$-0.00318452\pi$
$998$	−9.68208	+	4.01045i	−0.306481	+	0.126949i
$999$		−	32.1258i		−	1.01642i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.m.e.151.5		24
5.2	odd	4		85.2.m.a.49.2	✓	24
5.3	odd	4		85.2.m.a.49.5	yes	24
5.4	even	2	inner	425.2.m.e.151.2		24
15.2	even	4		765.2.bh.b.559.5		24
15.8	even	4		765.2.bh.b.559.2		24
17.5	odd	16		7225.2.a.by.1.6		24
17.8	even	8	inner	425.2.m.e.76.5		24
17.12	odd	16		7225.2.a.by.1.5		24
85.8	odd	8		85.2.m.a.59.2	yes	24
85.12	even	16		1445.2.b.i.579.6		24
85.22	even	16		1445.2.b.i.579.5		24
85.29	odd	16		7225.2.a.by.1.20		24
85.39	odd	16		7225.2.a.by.1.19		24
85.42	odd	8		85.2.m.a.59.5	yes	24
85.59	even	8	inner	425.2.m.e.76.2		24
85.63	even	16		1445.2.b.i.579.19		24
85.73	even	16		1445.2.b.i.579.20		24
255.8	even	8		765.2.bh.b.739.5		24
255.212	even	8		765.2.bh.b.739.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.m.a.49.2	✓	24	5.2	odd	4
85.2.m.a.49.5	yes	24	5.3	odd	4
85.2.m.a.59.2	yes	24	85.8	odd	8
85.2.m.a.59.5	yes	24	85.42	odd	8
425.2.m.e.76.2		24	85.59	even	8	inner
425.2.m.e.76.5		24	17.8	even	8	inner
425.2.m.e.151.2		24	5.4	even	2	inner
425.2.m.e.151.5		24	1.1	even	1	trivial
765.2.bh.b.559.2		24	15.8	even	4
765.2.bh.b.559.5		24	15.2	even	4
765.2.bh.b.739.2		24	255.212	even	8
765.2.bh.b.739.5		24	255.8	even	8
1445.2.b.i.579.5		24	85.22	even	16
1445.2.b.i.579.6		24	85.12	even	16
1445.2.b.i.579.19		24	85.63	even	16
1445.2.b.i.579.20		24	85.73	even	16
7225.2.a.by.1.5		24	17.12	odd	16
7225.2.a.by.1.6		24	17.5	odd	16
7225.2.a.by.1.19		24	85.39	odd	16
7225.2.a.by.1.20		24	85.29	odd	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.23200 + 1.23200i) q^{2} +(-0.229112 - 0.553124i) q^{3} +1.03565i q^{4} +(0.399184 - 0.963715i) q^{6} +(0.958968 + 0.397218i) q^{7} +(1.18808 - 1.18808i) q^{8} +(1.86787 - 1.86787i) q^{9} +(0.0292605 - 0.0706410i) q^{11} +(0.572843 - 0.237279i) q^{12} +2.86011i q^{13} +(0.692077 + 1.67082i) q^{14} +4.99873 q^{16} +(4.05747 + 0.732781i) q^{17} +4.60242 q^{18} +(-2.96308 - 2.96308i) q^{19} -0.621436i q^{21} +(0.123079 - 0.0509809i) q^{22} +(-2.27724 + 5.49775i) q^{23} +(-0.929359 - 0.384953i) q^{24} +(-3.52366 + 3.52366i) q^{26} +(-3.12049 - 1.29255i) q^{27} +(-0.411378 + 0.993155i) q^{28} +(-0.0817180 + 0.0338487i) q^{29} +(-0.928823 - 2.24238i) q^{31} +(3.78228 + 3.78228i) q^{32} -0.0457772 q^{33} +(4.09601 + 5.90159i) q^{34} +(1.93445 + 1.93445i) q^{36} +(3.63988 + 8.78745i) q^{37} -7.30103i q^{38} +(1.58200 - 0.655285i) q^{39} +(-7.74202 - 3.20685i) q^{41} +(0.765609 - 0.765609i) q^{42} +(0.612604 - 0.612604i) q^{43} +(0.0731594 + 0.0303036i) q^{44} +(-9.57880 + 3.96767i) q^{46} -8.33326i q^{47} +(-1.14527 - 2.76492i) q^{48} +(-4.18791 - 4.18791i) q^{49} +(-0.524293 - 2.41217i) q^{51} -2.96207 q^{52} +(-2.89277 - 2.89277i) q^{53} +(-2.25202 - 5.43686i) q^{54} +(1.61126 - 0.667405i) q^{56} +(-0.960076 + 2.31783i) q^{57} +(-0.142378 - 0.0589750i) q^{58} +(-6.48348 + 6.48348i) q^{59} +(-0.266392 - 0.110343i) q^{61} +(1.61830 - 3.90692i) q^{62} +(2.53317 - 1.04927i) q^{63} -0.677928i q^{64} +(-0.0563975 - 0.0563975i) q^{66} -12.8961 q^{67} +(-0.758905 + 4.20211i) q^{68} +3.56268 q^{69} +(5.05320 + 12.1995i) q^{71} -4.43835i q^{72} +(-6.04988 + 2.50594i) q^{73} +(-6.34181 + 15.3105i) q^{74} +(3.06871 - 3.06871i) q^{76} +(0.0561197 - 0.0561197i) q^{77} +(2.75633 + 1.14171i) q^{78} +(3.99465 - 9.64395i) q^{79} -5.90253i q^{81} +(-5.58733 - 13.4890i) q^{82} +(6.86298 + 6.86298i) q^{83} +0.643590 q^{84} +1.50946 q^{86} +(0.0374451 + 0.0374451i) q^{87} +(-0.0491634 - 0.118691i) q^{88} +0.106159i q^{89} +(-1.13609 + 2.74276i) q^{91} +(-5.69374 - 2.35843i) q^{92} +(-1.02751 + 1.02751i) q^{93} +(10.2666 - 10.2666i) q^{94} +(1.22551 - 2.95863i) q^{96} +(-7.91737 + 3.27948i) q^{97} -10.3190i q^{98} +(-0.0772933 - 0.186603i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{9} + 24 q^{14} + 8 q^{16} + 24 q^{19} - 32 q^{24} - 16 q^{26} - 24 q^{29} - 24 q^{31} - 8 q^{34} + 8 q^{36} + 24 q^{39} - 48 q^{41} - 72 q^{44} - 16 q^{46} - 48 q^{49} - 32 q^{54} + 24 q^{56}+ \cdots + 80 q^{99}+O(q^{100}) \) 24 * q + 8 * q^9 + 24 * q^14 + 8 * q^16 + 24 * q^19 - 32 * q^24 - 16 * q^26 - 24 * q^29 - 24 * q^31 - 8 * q^34 + 8 * q^36 + 24 * q^39 - 48 * q^41 - 72 * q^44 - 16 * q^46 - 48 * q^49 - 32 * q^54 + 24 * q^56 + 48 * q^59 + 16 * q^61 - 96 * q^66 - 32 * q^69 + 16 * q^71 + 64 * q^74 - 24 * q^76 + 72 * q^79 + 96 * q^84 - 8 * q^91 + 40 * q^94 + 96 * q^96 + 80 * q^99

Introduction

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